`(sin x)/(sin x)=lambda cos(x)/(8)-cos(x)/(4)cos(x)/(2),` then `lambda`=`

8.sin(x/8). cos (x/2).cos (x/4).cos (x/8) =

intcos.(x)/(16)cos.(x)/(8)cos.(x)/(4)cos.(x)/(2)sin.(x)/(16)dx=

8 * sin ((x) / (8)) * cos ((x) / (2)) * cos ((x) / (4)) * cos ((x) / (8)) =

cos x cos((x)/(2))-cos3x cos((9x)/(2))=sin7x sin8x

((sin x+cos x)^(2))/((sin x-cos x)^(2))

The curve satisfying the differential equation sin(x^(3))e^(y)dy+3x^(2)cos(x^(3))e^(y)dx=x sin (x^(2))dx C is the constant of integration is lambda sin (x^(3))e^(y)+cos(x^(2))=C . Then, the value of lambda is

int(sin x)/(cos^(3)x(1+cos^(8)x)^(3/4))*dx=f(x)*(1+cos^(8)x)^((1)/(lambda))+c Then lambda*f((pi)/(3))=

int(sin x)/(cos^(3)x(1+cos^(8)x)^(3/4))*dx=f(x)*(1+cos^(8)x)^((1)/(lambda))+c Then lambda*f((pi)/(3))=

int(sin^(8)x-cos^(8)x)/(1-2sin^(2)x cos^(2)x)dx=

If fundamental period of the functions f(x)=sin^(2)x+cos^(4)x and g(x)=cos(sin2x)+cos(cos2x) are lambda_(1) and lambda_(2) respectively then (lambda_(1))/(lambda_(2))=